{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZDKRVAZAIKGUKW4IMLVEQEQJSP","short_pith_number":"pith:ZDKRVAZA","canonical_record":{"source":{"id":"1002.2708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-13T14:26:52Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","nlin.SI"],"title_canon_sha256":"06b3385af4da9c68faf662763e3d993f8f5ef0594705aa0fca7811f8faafb000","abstract_canon_sha256":"72f7cb67979688ad51523cfe3635c697b6a0f30c673538a74f31fb0ecd275bb9"},"schema_version":"1.0"},"canonical_sha256":"c8d51a8320428d455b8862ea48120993f877ba36c0b2f2a5774182970fbe9822","source":{"kind":"arxiv","id":"1002.2708","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2708","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2708v2","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2708","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZDKRVAZAIKGU","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZDKRVAZAIKGUKW4I","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZDKRVAZA","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZDKRVAZAIKGUKW4IMLVEQEQJSP","target":"record","payload":{"canonical_record":{"source":{"id":"1002.2708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-13T14:26:52Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","nlin.SI"],"title_canon_sha256":"06b3385af4da9c68faf662763e3d993f8f5ef0594705aa0fca7811f8faafb000","abstract_canon_sha256":"72f7cb67979688ad51523cfe3635c697b6a0f30c673538a74f31fb0ecd275bb9"},"schema_version":"1.0"},"canonical_sha256":"c8d51a8320428d455b8862ea48120993f877ba36c0b2f2a5774182970fbe9822","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:12.665633Z","signature_b64":"enCaSJnlWpLnS1ysgyLJpcb+CRloIak4i/55hGAFUazp3aNIQ2H3DNhx9VkYkydCjj822fSaO5Jj1CxKBTI/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8d51a8320428d455b8862ea48120993f877ba36c0b2f2a5774182970fbe9822","last_reissued_at":"2026-05-18T04:30:12.665082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:12.665082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.2708","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x7ifolxwqJ13wUz4NxV4+shkYEeafSuottpY47NTPjw19l1mgLpgWZ22FB55E0750trlZKS0G9XzsFjOP/KsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:21:54.873704Z"},"content_sha256":"1c869a0f3ba1022e987032107eac648d467482749c778043f75f1eba2de74b1a","schema_version":"1.0","event_id":"sha256:1c869a0f3ba1022e987032107eac648d467482749c778043f75f1eba2de74b1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZDKRVAZAIKGUKW4IMLVEQEQJSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical and grand canonical partition functions of Dyson gases as tau-functions of integrable hierarchies and their fermionic realization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"A. Zabrodin","submitted_at":"2010-02-13T14:26:52Z","abstract_excerpt":"The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms of free fermionic operators. This representation provides an explicit identification of the partition function with a tau-function of the 2D Toda lattice hierarchy. Its dispersionless (quasiclassical) limit yields the tau-function for analytic curves encoding the integrable structure of the inverse potential problem and parametric conformal maps. A similar fermionic realization of partition functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2708","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M1UJo3FJIWntHEnHAxDwsWdNiccGvwrPFRLvv/1a/MiO7+lIX7WUryRyQdFORafpHbmUEJEyodtmNiOd51lgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:21:54.874057Z"},"content_sha256":"2727064f64930704343da636548ebf15786d58fc3b61d1f92e3f9eb72a8d9f6f","schema_version":"1.0","event_id":"sha256:2727064f64930704343da636548ebf15786d58fc3b61d1f92e3f9eb72a8d9f6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZDKRVAZAIKGUKW4IMLVEQEQJSP/bundle.json","state_url":"https://pith.science/pith/ZDKRVAZAIKGUKW4IMLVEQEQJSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZDKRVAZAIKGUKW4IMLVEQEQJSP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T12:21:54Z","links":{"resolver":"https://pith.science/pith/ZDKRVAZAIKGUKW4IMLVEQEQJSP","bundle":"https://pith.science/pith/ZDKRVAZAIKGUKW4IMLVEQEQJSP/bundle.json","state":"https://pith.science/pith/ZDKRVAZAIKGUKW4IMLVEQEQJSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZDKRVAZAIKGUKW4IMLVEQEQJSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZDKRVAZAIKGUKW4IMLVEQEQJSP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"72f7cb67979688ad51523cfe3635c697b6a0f30c673538a74f31fb0ecd275bb9","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-13T14:26:52Z","title_canon_sha256":"06b3385af4da9c68faf662763e3d993f8f5ef0594705aa0fca7811f8faafb000"},"schema_version":"1.0","source":{"id":"1002.2708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2708","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2708v2","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2708","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZDKRVAZAIKGU","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZDKRVAZAIKGUKW4I","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZDKRVAZA","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:2727064f64930704343da636548ebf15786d58fc3b61d1f92e3f9eb72a8d9f6f","target":"graph","created_at":"2026-05-18T04:30:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms of free fermionic operators. This representation provides an explicit identification of the partition function with a tau-function of the 2D Toda lattice hierarchy. Its dispersionless (quasiclassical) limit yields the tau-function for analytic curves encoding the integrable structure of the inverse potential problem and parametric conformal maps. A similar fermionic realization of partition functio","authors_text":"A. Zabrodin","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-13T14:26:52Z","title":"Canonical and grand canonical partition functions of Dyson gases as tau-functions of integrable hierarchies and their fermionic realization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2708","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1c869a0f3ba1022e987032107eac648d467482749c778043f75f1eba2de74b1a","target":"record","created_at":"2026-05-18T04:30:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"72f7cb67979688ad51523cfe3635c697b6a0f30c673538a74f31fb0ecd275bb9","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-13T14:26:52Z","title_canon_sha256":"06b3385af4da9c68faf662763e3d993f8f5ef0594705aa0fca7811f8faafb000"},"schema_version":"1.0","source":{"id":"1002.2708","kind":"arxiv","version":2}},"canonical_sha256":"c8d51a8320428d455b8862ea48120993f877ba36c0b2f2a5774182970fbe9822","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8d51a8320428d455b8862ea48120993f877ba36c0b2f2a5774182970fbe9822","first_computed_at":"2026-05-18T04:30:12.665082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:12.665082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"enCaSJnlWpLnS1ysgyLJpcb+CRloIak4i/55hGAFUazp3aNIQ2H3DNhx9VkYkydCjj822fSaO5Jj1CxKBTI/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:12.665633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.2708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c869a0f3ba1022e987032107eac648d467482749c778043f75f1eba2de74b1a","sha256:2727064f64930704343da636548ebf15786d58fc3b61d1f92e3f9eb72a8d9f6f"],"state_sha256":"c5e1a4c10050cc113cca2d358f2bb41f039b246cfda4ba37b6a5f35059743418"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n4Q4sCgA/WrCA0YZJkTfThMm/8dh8lUng903GN1BlNtqbY3Qb3FfVhe5p6fPP4nF7zp3E/kALPQ7P2wkxeaABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:21:54.875968Z","bundle_sha256":"5c5ecc682d09d26b34822d355b7884160445ece72c730742423a9eb668672634"}}